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MEN"  OF MATHEMATICS

Such are the theory of finite groups, the mathematical theory
of the infinite, and parts of the theory of probabilities and the
higher arithmetic. So it is not astonishing that large tracts of
what a candidate is required to know for entrance to a technical
or scientific school, or even for graduation from the same, are
less than worthless for a mathematical career. This accounts
for Hermite's spectacular success as a budding mathematician
and his narrow escape from complete disaster as an examinee.

Late in 1842, at the age of twenty, Hermite sat for the en-
trance examinations to the ficole Polytechnique. He passed,
but only as sixty-eighth in order of merit. Already he was a
vastly better mathematician than some of the men who
examined him were, or were ever to become. The humiliating
outcome of this test made an impression on the young master
which all the triumphs of his manhood never effaced.

Hermite stayed only one year at the Polytechnique. It was
not his head that disqualified him but his lame foot which,
according to a ruling of the authorities, unfitted him for any of
the positions open to successful students of the school. Perhaps
it is as well that Hermite was thrown out; he was an ardent
patriot and might easily have been embroiled in one or other
of the political or military rows so precious to the effervescent
French temperament. However, the year was by no means
wasted. Instead of slaving over descriptive geometry, which
he hated, Hermite spent his time on Abelian functions, then
(1842) perhaps the topic of outstanding interest and importance
to the great mathematicians of Europe. He had also made the
acquaintance of Joseph Liouville (1809-82), a first-class
mathematician and editor of the Journal des Mathematiques.

Liouville recognized genius when he saw it* In passing it may
be amusing to recall that Liouville inspired William Thomson,
Lord Kelvin, the famous Scotch physicist, to one of the most
satisfying definitions of a mathematician that has ever been
given, 'Do you know what a mathematician is?' Kelvin once
asked a class. He stepped to the board and wrote

Putting his finger on what he had written, he turned to the
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